Descriptions of dreams and the timings of associated REM-sleep stages have been recorded over a long period of time (more than 1 year). Invariance of the probability distribution of awakenings within a certain period of ultradian rhythm over random sample reveals the influence of the rhythm on the timings of the sleep stages.
Keywords: REM-sleep stage, noomatter, timings of awakening, ultradian rhythm.
2. Experimental procedures and treatment
5. Devices and tools
6. Steins asteroid as the source of hypothetic rhythm
1. IntroductionThe biorhythms in living organisms are stimulated by the circadian rhythms of geological origin , rhythms of cosmic radiation and other rhythms of environment. Since the present work has been executed as part of investigation into the correlations between dreams and astronomic phenomena, here under consideration are rhythms associated exclusively with the physiology of human sleep. To rhythms of the type we can attribute the ultradian rhythms that stimulate the 90-100 min cycles known as rapid eye movement (REM)-sleep stages and consisting in succession of slow and rapid sleep stages. However, in the present research not the periodicity is stressed but rather the shifts of sleep stages and phases are important as related to the global time; most likely these shifts also depend on some external rhythmical drives.
The aim of the present investigation is/was to reveal the factors that point – directly or indirectly – to the existence of rhythms belonging to the ultradian range and affecting the position of rapid eye movement (REM) stage of human sleep on the scale of global time, since it is the phase during which a person sees dreams.
To achieve this aim, the on-location timing measurements of REM phases have been run in order to obtain the probability distribution for the occurrence of events within the time interval equal to the period of a rhythm presumably located in the ultradian range.
Terms and notions accepted in the text
T – the full calendar period of observation: the time span from April 1, 2013 to May 20, 2014, during which the noises produced by body movements of a sleeping person under test were recorded, read from the end REM-phase audiogram and placed in the database together with the texts of associated dreams.
Ti (i=1,2,3,4) – Lengths of the calendar time as proportions of the full calendar period of observation; these lengths have been selected assuming that there is the equal number of events in each of the lengths – both intersecting and non-intersecting within the full calendar period of observations T. The notion was introduced into the calculation methods in order to estimate the invariance of distributions with regard to the scale of calendar time.
∆Τi – The 9.09 min time span to which the lengths of calendar time Ti are broken down; the span is considered as a period of ultradian rhythm.
ΦT (t) – The density distribution of awakings over the full period T: ΦΤ1 (t) — over the time length T1, ΦT2 (t) — over the time length T2, and so on, with t being the time from the beginning of span Τ, Τi.
Φ∆Τi (t) – The probability distribution for falling of the value t within a minute interval on the time span ∆Τ. The distribution Φ∆Τi (t) is obtained by making summation of those for each separate span ∆Τ within the length Ti of calendar time, with t being the time from the beginning of span ∆Τi .
2. Experimental procedures and treatment
The tests proceeded as follows. During the sleep of a testee under test all the noises from her body movements were recorded on a dictaphone, the recorded audiogram was analyzed, and singular points on the audiogram that correlate with the REM-phase end time were entered into the database. If after awaking the testee was able to transmit the contents of her dreams, this communication was also stored in the dictaphone’s memory. The awaking time was recorded with the accuracy of ± 5 s from the global time maintained in the equipment by synchronization via internet.
The length of rhythm span ∆Τ – whose influence on he shift of REM-sleep stages is the subject of investigation – was determined by analyzing characteristic data shown in Fig. 1, where the lines of intersection of the Earth’s surface by the ecliptic planes at the awaking moments are in some sections alternating at approx. equal time intervals. The calculation of this period of alternating events has given the result ∆Τ=9.09 min.
At processing the data, the length of calendar time Ti of the observation period is broken down into intervals ∆Τ, and for each event the shift t is calculated from the beginning of the interval to which a given event belongs. Next, considering the data set as a series of random numbers, we broke down the period ∆Τ into equal time intervals and count the frequencies of events in each step. In such a way we obtain an interval series with the absolute frequencies, and, having divided each frequency by the overall number of events in the period, we derive some relative frequencies – i.e. the probability of the event’s falling into the dividing interval. After that, the calculations are performed with plotting the curves (see below) of probability distribution for falling of the event’s value into the unit of measurement over period ∆Τ of the rhythm.
All singular points obtained in the analysis of audiograms are (sub)divided into the completed (1594 events) and uncompleted (1544 events) awakings. Not every completion of the REM phase is followed by full awaking with subsequent readiness to communicate the memorized dream.
We will consider separately the treatment results for some groups from these two categories.
3.1. Completed awakings. In the case when the end of REM-sleep stage results in full awaking and the testee is able to dictate the contents of a memorized dream, on audiogram this event is categorized as the full awaking. In this category total 1594 events have been collected. To estimate the invariance relative to the calendar time scale, the calculations have been performed for four variants of dividing the full calendar period T of observation into the calculated lengths of time Ti.
The full period of calendar time of observation.
Fig. 2 shows the diagram of probability density distribution Φ∆Τ(t) for completed awakings over time interval ∆Τ for the full observation time T from April 1, 2013 to May 20, 2014. On the diagram the areas/domains with clearly seen maxima of the event density are designated 1 and 2.
The observation period T is divided into two non-overlapping intervals T1 and T2.
The condition of dividing is the equal number of events within each of the intervals. The treatment result is presented in Fig. 3a, where the explicitly expressed maxima in distribution curves for both intervals are located approx. in one and the same sector of time span ∆Τ. The scheme of dividing the full period T into two time intervals is shown in Fig. 3b.
The observation period is divided into three non-overlapping intervals T1,T2 and T3.
The condition of dividing is the equal number of events within each of the intervals. The treatment result is presented in Fig. 4a, where the explicitly expressed maxima in distribution curves for the three intervals are located approx. in one and the same sectors of time span ∆Τ. The scheme of dividing the full period T into three time intervals is shown in Fig. 4b.
The observation period is divided into four overlapping intervals (T1,T2, T3, T4).
The condition of dividing is the equal number of events within each of the intervals.
Fig. 5a shows the curves of distributions Φ∆Τ(t) for the four intervals, and Fig. 5b – the scheme of dividing the full period T into intervals. Here the distribution is also invariant with regard to the samples from the observation period.
3.2.Uncompleted awakings. In the process of treatment from the audiogram not only the events of the REM phase end were retrieved that are completed with awakings and recording the dream contents, but also other noises produced by the body movements of a sleeping person. These latter are estimated as the end of rapid sleep but without full awaking. The number of such type events revealed in the observation period is 1544. The treatment results are shown in Fig.6: a) the distribution curve for uncompleted awakings is given in comparison with that for completed in the period T; b) distribution curves for completed (blue) and uncompleted (orange) awakings within interval ∆Τ during the full observation period Τ.
4. DiscussionAnalysis of the probability distribution Φ∆Τ(t) over the time interval ∆Τ for awakings estimated as the end of REM-sleep stage with the completed and the uncompleted awaking allows for the inference that REM phases are connected with some external rhythm of unknown nature. Such inference relies upon the invariance of distribution Φ∆Τ(t) type for time spans Ti (i=1,2,3,4). The central maximum in the distribution curve presents the upper part of normal distribution, which means that there is some common source of rhythm. The smaller maxuma are presumably indicative of less intensive rhythms.
The results presented here have been obtained from the author’s observations; therefore, so far we might consider the observed pattern of probability distribution Φ∆Τ(t) as some individual characteristic.
Probable sources of the ultradian rhythm
One of the most probable sources of an unknown rhythm could be variations of the geomagnetic field vector in the frequency range 0.5-3.0 mHz (5-30 min periods) that synchronizes the heart rhythms . This means that the period ∆Τ=9.09 min of the of hypothetical rhythm falls within these limits. Results of the mentioned work imply that in the case under consideration we should proceed from the existence of several rhythms in the range from minutes to tens of minutes.
The rhythm can also be stemmed from asteroids and the planets of solar system – see, e.g., Ch.6 (Steins asteroid).
One more suggestion is that the origin of ultradian rhythm is some carrier wave frequency in the procedure of synchronization and connection of the sub-consciousness and the noomatter – its existence was proposed in .
Interaction of an external source of the rhythm and the subconsciousness within a sleep stage proceeds in several steps in a nocturnal period, which are observed as phases of human sleep. In the first phases (the slow sleep) the synchronization procedure is started up as search for and adjustment to the external rhythm, and the mentioned above connection happens at the beginning of a REM phase. On completion of this phase the connection closes.
In further investigations the following is to be done:
▪ To use encephalograph for determination of timing for all sleep stages, which would give an unambiguous identification of the events than audio-recording. This would allow revealing the contribution of each sleep stage to the procedures of synchronization and interaction between subconsciousness and the source of external rhythm. In turn, this will considerably extend the present-day notions about the influence of external rhythm on the dynamics of sleep stages as well as about the general properties and the functional features of sleep stages and phases.
▪ To perform calculations to reveal correlations with the motion of celestial bodies as parameters of the awaking density distribution within the periods of exposure to external actions and as well as those relating to the contents of dreams.
▪ To extend the scope of using mathematical methods.
▪ To recruit volunteers for investigations with the aim to obtain the data that would allow revealing the dependence of rhythm parameters on individual features.
5. Devices and Tools
In the course of research the following equipment and software have been used:
1) Instruments. Dictaphone Sony IC Recorder ICD-UX512, memory 2 Gb, MP3 48 K/s, with connection to computer via USB.
· Sony Sound Organizer – the program for representation of audio-signal in the form of graphic audiogram.
· The author’s software for calculating the ephemerides of celestial bodies with graphical deduction of results.
6. Asteroid Steins as the source of hypothetic rhythm
The nature of the rhythm affecting the proceeding of sleep stages is unknown. As a variant, we will presume the source of this rhythm to be one of several celestial bodies of the solar system whose rotation generates signals exerting influence of the dynamics of human sleep. Presumably, this could be the asteroid discovered as long ago as 1969 and investigated in 2008 by means of interplanetary spacecraft “Rosetta” of European Space Agency (ESA): when this apparatus was flying by the asteroid, at shooting for seven minutes its 3D image was obtained. As seen on the photo from , the shape of the asteroid is close to that of diamond. Consequently, at the asteroid’s rotation the Earth planet will periodically be intersected by the beam entering through the top face (called the surface element of the crown of asteroid-diamond) and refracted by the cut side faces of the diamond’s crown and pavilion.
Estimation of the number of asteroid faces. Let us suppose that asteroid Šteins (named after Kārlis Šteins, a Latvian and Soviet astronomer) is the source of the exorhythm affecting the timings of REM phase. Using the orbital parameters of Šteins 2867, class E  and having performed all the necessary calculations with the rhythm’s taken 9.09 min we obtain the figure of 39.9. This means that from the Earth 40 flashes at the interval of 9.09 min are to be observed in one turn of the asteroid-diamond about its axis (6 h 2 min). To some extent these calculations allow judging/estimating the number of faces in the main-belt of diamond. The central maximum of the density distribution of events in Fig. 2 corresponds to the basic frequency of the rhythm, while the secondary maxima are either distortions due to irregular shape of the asteroid or are produced by reflections from the faces of extra belts of the crystal.
The author expresses his gratitude to Anthony Goddard for help in abstract translation into English, E. Shirova in translation main text body into English and L.A. Аntipina for moral support – especially in the initial stages of work.
 T.A. Zenchenko, А.А. Medvedeva, N.I. Horseva, Т.K. Breus. Synchronization of indicators of human heart rhythm with variations of geomagnetic field in the frequency range 0.5–3.0 mHz. Available at: www.biophys.ru/archive/rhythm-00001.pdf; (in Russian).
 Kotchnev O.D. Noomatter as the highest form of matter. Проза.ру., 15 марта 2014 г. Available at: http://www.proza.ru/2014/03/15/2013 (in Russian)
 Richard C. Hoagland. The Hidden Story of The "Asteroid" Steins' Encounter. Available at: http://www.bibliotecapleyades.net/ciencia/ciencia_asteroids_comets15.htm
 Wikipedia, (2867) Šteins. Available at:https://en.wikipedia.org/wiki/2867_%C5%A0teins
For the material published see also:
1) www.proza.ru -Свидетельство о публикации № 214070101695
2) www.proza.ru (eng) -Свидетельство о публикации № 214092801635
3) knigotopia.ru - PDF
4) knigotopia.ru(eng,rus)- PDF
6) www.samolit.com - ePub, Fb2
7) www.samolit.com (eng) - ePub, Fb2
9) samlib.ru(eng,rus) - Fb2
12) www.vixra.org(eng, rus) - PDF
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